’s glue logic for computing logical form dynamic. This allows us to model a dialogue agent’s understanding of what the update of the semantic representation of the dialogue would be after his next contribution, including the effects of the rhetorical moves that he is contemplating performing next. This is a pre-requisite for developing a model of how agents reason about what to say next. We make the glue logic dynamic by using a dynamic public announcement logic ( pal ). We (...) extend pal with a particular variety of default reasoning suited to reasoning about discourse—this default reasoning being an essential component of inferring the pragmatic effects of one’s dialogue moves. We add to the pal language a new type of announcement, known as ceteris paribus announcement, and this is used to model how an agent anticipates the (default) pragmatic effects of his next dialogue move. Our extended pal validates certain intuitive patterns of default inference that existing pal s for practical reasoning do not. We prove that the dynamic glue logic has a pspace validity problem, and as such is no more complex than pal with multiple $${\square}$$ operators. (shrink)

Wittgenstein initially endorsed but then abandoned, by the time of “Some Remarks on Logical Form”, the view that elementary propositions are logically independent. In this paper it is argued that the doctrine of logical independence is in fact inconsistent with the intuitions and examples that motivated the picture theory of the Tractatus Logico-Philosophicus. This leaves the question of whether the logical independence of elementary propositions can be reconciled with the theory itself; the paper explores some interpretations of the early Wittgenstein (...) with which this is, and others with which it is not, consistent. (shrink)

The author puts forth an approach to propositional attitude contexts based upon the view that one does not have beliefs of ordinary extensional entitiessimpliciter. Rather, one has beliefs of such entities as presented in various manners. Roughly, these are treated as beliefs of ordered pairs — the first member of which is the ordinary extensional entity and the second member of which is a predicate that it satisfies. Such an approach has no difficulties with problems involving identity, such as of (...) The Morning Star and The Evening Star (section 1). Given the second members of the pairs, the modes of presentation, it is quite natural to allow exportation everywhere. There is no need for essentialism. (One also can have non-essentialistic modal logic if one grants analyticity or the like.) (section 2). Given that the second member of the pair need only be one that is satisfied by the entity that is the first member (and need not be specificative), the method has no difficulties when one is concerned only with discriminations (and not specifications) (section 3). When this method is combined with the Frege-Carnap method of descriptions, fictional entities can be accommodated; Goodman''s unicorn-picture and the like can be brought within a Tarskian semantics; and Geach''s difficulties with intentional identity appear to be handled (section 4). Given the author''s ordered pair construals, there appears to be no additional need for notional construals; i.e., the author''s one unified method appears satisfactory for dealing with both traditionalde re (relational) andde dicto (notional) construals. The Paradox of the Knower and the like do not appear formulatable against the author''s approach. (section 5). The author also argues against the basic principles behind the Church-Langford translation argument (section 6). (shrink)

Many commentators have attempted to say, more clearly than Wittgenstein did in his Tractatus logico-philosophicus, what sort of things the ‘simple objects’ spoken of in that book are. A minority approach, but in my view the correct one, is to reject all such attempts as misplaced. The Tractarian notion of an object is categorially indeterminate: in contrast with both Frege's and Russell's practice, it is not the logician's task to give a specific categorial account of the internal structure of elementary (...) propositions or atomic facts, nor, correlatively, to give an account of the forms of simple objects. The few commentators who have hitherto maintained this view have mainly devoted themselves to establishing that this was Wittgenstein's intention, and do not much address the question whyWittgenstein held that it is not the logician's business to say what the objects are. The present paper means to fill this lacuna by placing this view in the context of the Tractatus's treatment of logic generally, and in particular by connecting it with Wittgenstein's treatment of generality and with his reaction to Russell's approach to logical form. (shrink)

These are not just tricks or puzzles, but are intimately connected with some of the liveliest and most basic philosophical disputes about logical form, ...

Carruthers’ argument depends on viewing logical form as a linguistic level. But logical form is typically viewed as underpinning general purpose inference, and hence as having no particular connection to language processing. If logical form is tied directly to language, two problems arise: a logical problem concerning language acquisition and the empirical problem that aphasics appear capable of cross-modular reasoning.

In Kant’s logical texts the reference of the form of the judgment to an “unknown = x” (B 13) is well known, but its understanding remains far from consensual. Due to the universality of all concepts, the subject as much as the predicate, in the form S is P, is regarded as predicate of the x, which, in turn, is regarded as the subject of the judgment (Rx 3921, Rx 4634). In the CPR, particularly in the text on the “logical (...) use of the understanding” (B 92-4), this Kantian interpretation of the subject-predicate relation leads to the question about the relations that must hold between intuition and concept in the judgment. In contrast to intuition, if no concept, due to its universal character, refers immediately to an object, how should we understand the relations of subject and predicate to one another, as well as their relations to intuition, which corresponds to the very special individuality of that object in general = x? In short, the question at hand is to understand by what means could something completely indeterminate be represented in the judgment through the concepts of subject and predicate. (shrink)

Book Information Logical Form and Language. Edited by G. Preyer and G. Peter. Clarendon Press. Oxford. 2002. Pp. x + 512. Hardback, £55. Paperback, £19.99.

First order logic does not distinguish between different forms of universal generalization; in this paper I argue that lawlike and accidental generalizations (broadly construed) have a different logical form, and that this distinction is syntactically marked in English. I then consider the relevance of this broader conception of lawlikeness to the philosophy of science.

An attractive semantic theory presented by Richard K. Larson and Peter Ludlow takes a report of propositional attitudes, e.g 'Tom believes Judy Garland sang', to report a believing relation between Tom and an interpreted logical form constructed from 'Judy Garland sang'. We briefly outline the semantic theory and indicate its attractions. However, the definition of interpreted logical forms given by Larson and Ludlow is shown to be faulty, and an alternative definition is offered which matches their intentions. This definition is (...) then shown to imply that Tom does not know his own mind, a result without intuitive support. A third definition is offered to deal with this problem. (shrink)

Vernacularism is the view that logical forms are fundamentally assigned to natural language expressions, and are only derivatively assigned to anything else, e.g., propositions, mental representations, expressions of symbolic logic, etc. In this paper, we argue that Vernacularism is not as plausible as it first appears because of non-sentential speech. More specifically, there are argument-premises, meant by speakers of non-sentences, for which no natural language paraphrase is readily available in the language used by the speaker and the hearer. The speaker (...) can intend this proposition and the hearer can recover it (and its logical form). Since they cannot, by hypothesis, be doing this by using a sentence of their shared language, the proposition-meant has its logical form non-derivatively, which falsifies Vernacularism. We conclude the paper with a brief review of the debate on incomplete definite descriptions in which Vernacularism is assumed as a suppressed premise. (shrink)

Truth and Meaning is a classic collection of original essays on fundamental questions in the philosophy of language.

A Logical Form (LF) is a syntactic structure that is interpreted by the semantic component. For a particular structure to be a possible LF it has to be possible for syntax to generate it and for semantics to interpret it. The study of LF must therefore take into account both assumptions about syntax and about semantics, and since there is much disagreement in both areas, disagreements on LF have been plentiful. This makes the task of writing a survey article in (...) the field fairly difficult, a difficulty that is amplified by the amount of material that needs to be covered if the result is going to be in any way representative. My response to this difficulty is to limit my objectives. As a start, I will confine myself to issues relating to the syntactic positions of Quantificational Noun Phrases (QNPs) at LF and to various interpretive consequences. But even within these relatively narrow confines, I will not attempt anything close to a comprehensive survey. Instead my goal will be restricted to the presentation of one leading idea and to the discussion of some evidence that might bear on it.1 Much research on the nature of LF has consisted in attempts to account for the meaning of sentences containing QNPs. (shrink)

It is widely believed that existential quantifiers can bring about the semantic effects of a scope which is wider than their actual syntactic scope (See Fodor & Sag (1982), Cresti (1995), Kratzer (1995), Reinhart (1995) and Winter (1995), among many others.) On the other hand, it is assumed that the syntactic scope of universal quantifiers can be determined unequivocally by the semantics. This paper shows that this second assumption is wrong; universal quantifiers can also bring about scope illusions, though in (...) a very specific environment. In particular, we argue that in the environment of generic tense, universal quantifiers can show the semantic effects of a scope which is wider than the one that is actually realized at LF. Our argument has four steps. First, we show that in generic contexts, universal quantifiers escape standard “scope-islands” (Section 1). Second, we show how the effects of wide scope in generic contexts can be achieved without syntactic wide scope (Section 2.1). Third, we show that this result is actually forced on us, once we take seriously certain independent issues concerning the interpretation of generic tense (Sections 2.2 - 2.4). Finally, the semantics of generic tense and, in particular, its interaction with focus, will yield some intricate new predictions, which, as we show, are borne out (Sections 3 - 5). (shrink)

Following Popper on the measure of content, we will combine the concept of logical probability, developed in the nineteenth century, with logical form, and we will answer some objections of Elias to the systematization of Popper's idea by Bar-Hillel and Carnap. We were led along this path by a novel by Isaac Asimov, the biochemist, medical school professor, science fiction writer, and popular science writer—a true polymath with over 400 books to his credit. Elias was concerned that Bar-Hillel and Carnap's (...) theory of semantic content had no philosophical import, no unique properties, and no applications. We will suggest three areas of philosophical import, a unique property based on differences as explained by Peter Milne, and some applications in the general area of abstracting or summarization. We will also suggest that automated language-to-logical-form converters are feasible, necessary for the achievement of various ends, and desirable for the achievement of other ends. In the entire discussion of logical form, we will rely entirely on modern, classical (i.e., two-valued, truth-functional) logic alone, including that most vexatious of connectives, "if." We will close our work with an argument referred to in favor of > from our earlier work, in particular, and truth-functionality, more generally. The connection between the material on content in the first part of this book and the material on a truth-functional approach to logical form in the second part of this book is that the former material presupposes that a certain subset of declarative language is, in fact, truth-functional, a view that is particularly hard to defend for "if," and it is just that defense that is taken up in the second part. This book consists of ten published pieces, as well as three introductory units, and three concluding sections or units. (shrink)

Abstract is given in the paper itself, which see.

This paper gives the rationales behind the two extensive papers entitled "Abstracts from Logical Form".

Abstract is given in the paper itself, which see.

A theory of reference may be either an analysis of reference or merely an account of the correct use of the verb "refer". If we define the validity of arguments in the standard way, in terms of assignments of individuals and sets to the nonlogical vocabulary of the language, then we will be committed to seeking an analysis of reference. Those who prefer a metalinguistic account, therefore, will desire an alternative to standard semantics. One alternative is the Quinean conception of (...) logical validity as essentially a matter of logical form. Another alternative is Leblanc's truth-value semantics. But these prove to be either inadequate for purposes of metatheory or philosophically unsatisfactory. This paper shows how validity (i.e., semantic consequence) may be defined in a way that avoid the problems facing these other alternatives to standard semantics and also permits a metalinguistic account of reference. The validity of arguments is treated as a matter of logical form, but validity for forms is defined on analogy with the definition of semantic consequence in truth-value semantics. (A more radical kind of semantics without reference is the context logical approach represented in several of my other publications.). (shrink)

We discuss Hintikka’s Thesis [Hintikka 1973] that there exist natural language sentences which require non–linear quantification to express their logical form. For example.

This paper claims that there is a plausible sense in which validity is a matter of truth preservation relative to interpretations of the sentences that occur in an argument, although it is not the sense one might have in mind. §1 outlines three independent problems: the first is the paradox of the sorites, the second concerns the fallacy of equivocation, and the third arises in connection with the standard treatment of indexicals. §2 elucidates the claim about validity, while §§3-5 show (...) how the three problems outlined can be handled in accordance with it. §6 explains how the claim squares with the traditional idea that validity is related to formality, and in particular with a broadly accepted definition based on that idea, the model-theoretic definition of logical consequence. Unlike other works on the subject, this paper does not focus on necessity. It is not its intention to provide a characterization of necessity that conforms to some ideal of rigour or to some pre-theoretical understanding of validity. What follows can be taken as conditional on the assumption that such a characterization can be provided. (shrink)

The term ‘logical form’ has been called on to serve a wide range of purposes in philosophy, and it would be too ambitious to try to survey all of them in a single essay. Instead, I will focus on just one conception of logical form that has occupied a central place in the philosophy of language, and in particular in the philosophical study of linguistic meaning. This is what I will call the classical conception of logical form. The classical conception, (...) as I will present it in section 1, has (either explicitly or implicitly) shaped a great deal of important philosophical work in semantic theory. But it has come under fire in recent decades, and in sections 2 and 3 I will discuss two of the recent challenges that I take to be most interesting and significant. (shrink)

Notice that each of (1)–(4) is an instance of a more general pattern. For example, we could replace ‘black’ in (1) with any of a wide range of other adjectives such as ‘furry’ or ‘hungry’ or ‘three-legged’, without rendering the entailment invalid or any less obvious. Similarly, there are a number of verbs that occur in entailments parallel to (3): ‘Moe boiled the water; so the water boiled’; ‘Bart blew up the school; so the school blew up’; ‘Homer sank the (...) boat; so the boat sank’ and so on. (shrink)

... and new questions in philosophical logic arose, when Russell introduced his ... whether Scott is the author of Waverley without wishing to know whether ..

Everyday reasoning is replete with arguments which, though not logically valid, nonetheless harbor a measure of credibility in their own right. Here the claim that such arguments force us to acknowledge material validity, in addition to logical validity, is advanced, and criteria that attempt to unpack this concept are examined in detail. Of special concern is the effort to model these criteria on explications of logical validity that rely on notions of substitutivity and logical form. It is argued, however, that (...) such a parallel is not easily located and that it is uncertain that a construal of material validity can be fashioned after traditional accounts of logical validity. Attention is also given to the topics of enthymemes and to the proper domain of logic. (shrink)

The positions of Frege, Russell and Wittgenstein on the priority of complexes over (propositional) functions are sketched, challenging those who take the "judgment centered" aspects of the Tractatus to be inherited from Frege not Russell. Frege's views on the priority of judgments are problematic, and unlike Wittgenstein's. Russell's views on these matters, and their development, are discussed in detail, and shown to be more sophisticated than usually supposed. Certain misreadings of Russell, including those regarding the relationship between propositional functions and (...) universals, are exposed. Wittgenstein's and Russell's views on logical grammar are shown to be very similar. Russell's type theory does not countenance types of genuine entities nor metaphysical truths that cannot be put into words, contrary to conventional wisdom. I relate this to the debate over "inexpressible truths" in the Tractatus. I lastly comment on the changes to Russell's views brought about by Wittgenstein's influence. (shrink)

In 1903, in The Principles of Mathematics (PoM), Russell endorsed an account of classes whereupon a class fundamentally is to be considered many things, and not one, and used this thesis to explicate his first version of a theory of types, adding that it formed the logical justification for the grammatical distinction between singular and plural. The view, however, was short-lived; rejected before PoM even appeared in print. However, aside from mentions of a few misgivings, there is little evidence about (...) why he abandoned this view. In this paper, I speculate as to what those reasons were, and evaluate them in light of recent work and interest in plural logic. (shrink)

In this paper I propose a novel treatment of generic sentences, which proceeds by means of different levels of analysis. According to this account, all generic sentences (I-generics and D-generics alike) are initially treated in a uniform manner, as involving higher-order predication (following the work of George Boolos, James Higginbotham and Barry Schein on plurals). Their non-uniform character, however, re-emerges at subsequent levels of analysis, when the higher-order predications of the first level are cashed out in terms of quantification over (...) individuals: this last step, I suggest, involves knowledge concerning the lexical meaning of the predicates in question. (shrink)

Evidence is presented to show that the role of a generative grammar of a natural language is not merely to generate the grammatical sentences of that language, but also to relate them to their logical forms. The notion of logical form is to be made sense of in terms a natural logic, a logical for natural language, whose goals are to express all concepts capable of being expressed in natural language, to characterize all the valid inferences that can be made (...) in natural language, and to mesh with adequate linguistic descriptions of all natural languages. The latter requirement imposes empirical linguistic constraints on natural logic. A number of examples are discussed. (shrink)

Bertrand Russell, in the second of his 1914 Lowell lectures, Our Knowledge of the External World, asserted famously that ‘every philosophical problem, when it is subjected to the necessary analysis and purification, is found either to be not really philosophical at all, or else to be, in the sense in which we are using the word, logical’ (Russell 1993, p. 42). He went on to characterize that portion of logic that concerned the study of forms of propositions, or, as he (...) called them, ‘logical forms’. This portion of logic he called ‘philosophical logic’. Russell asserted that ... some kind of knowledge of logical forms, though with most people it is not explicit, is involved in all understanding of discourse. It is the business of philosophical logic to extract this knowledge from its concrete integuments, and to render it explicit and pure. (p. 53) Perhaps no one still endorses quite this grand a view of the role of logic and the investigation of logical form in philosophy. But talk of logical form retains a central role in analytic philosophy. Given its widespread use in philosophy and linguistics, it is rather surprising that the concept of logical form has not received more attention by philosophers than it has. The concern of this paper is to say something about what talk of logical form comes to, in a tradition that stretches back to (and arguably beyond) Russell’s use of that expression. This will not be exactly Russell’s conception. For we do not endorse Russell’s view that propositions are the bearers of logical form, or that appeal to propositions adds anything to our understanding of what talk of logical form comes to. But we will be concerned to provide an account responsive to the interests expressed by Russell in the above quotations, though one clarified of extraneous elements, and expressed precisely. For this purpose, it is important to note that the concern expressed by Russell in the above passages, as the surrounding text makes clear, is a concern not just with logic conceived narrowly as the study of logical terms, but with propositional form more generally, which includes, e.g., such features as those that correspond to the number of argument places in a propositional function, and the categories of objects which propositional.... (shrink)

This paper proposes and defends an Interface Transparency Thesis concerning how linguistic meanings are related to the cognitive systems that are used to evaluate sentences for truth/falsity: a declarative sentence is semantically associated with a canonical procedure for determining its truth value (cf. Dummett 1973, Horty 2007); and while this procedure need not be used as a verification strategy, competent speakers are biased towards strategies that directly reflect canonical specifications of truth conditions. Evidence in favor of this hypothesis comes from (...) a psycholinguistic experiment examining adult judgments concerning ‘Most of the dots are blue’. This sentence is true if and only if the number of blue dots exceeds the number of nonblue dots. But this leaves many issues unsettled—e.g., how the second cardinality is specified for purposes of understanding and/or verification: via the nonblue things, given a restriction to the dots, as in ‘|Dot(x) & ~Blue(x)|’; via the blue things, given the same restriction, and subtraction from the number of dots, as in ‘|Dot(x)| - |Dot(x) & Blue(x)|’; etc. We obtained evidence in favor of the second hypothesis. Participants saw displays of between 2 and 5 colors of dots for 150ms, with between 5 and 17 dots per color. Ratios of blue to non-blue dots ranged between 1:2 and 7:8, with half the trials containing more blue dots and half containing more nonblues. Results indicated use of the Approximate Number System (Dehaene 1997) in verification, with accuracy unaffected by the number of colors. It is independently known that for dots of up to 3 colors, the size of the total array is automatically computed. Given this fact and our result, we argue that the number of nonblue dots was specified via subtraction, and that sentences of the form ‘Most !s are "’ have corresponding meanings, with truth conditions canonically specified along the following lines: |!(x) & "(x)| > |!(x)| - |!(x) & "(x)|.. (shrink)

This work contains Peter Long's important essay, Logic, Form and Grammar , which resolves many difficulties for the logical form of an argument where the reasoning is hypothetical. Also included are two essays on classical problems in philosophical logic, relating to logical form and formal relations.

On this conception, the semantic types of its primitive terms and their mode of combination determine the logical form of a sentence as it relates to determining under what conditions it is true. We develop this idea in the framework of truth-theoretic semantics. We argue that the semantic form of a declarative sentence in a language L is revealed by a (canonical) proof of its T-sentence in an interpretive truth theory for L. We give a precise characterization of sameness of (...) logical form between any two declarative sentences in any two languages in terms of the notion of corresponding proofs in interpretive truth theories for the languages. We illustrate the utility of this approach with a number of examples. We then extend the characterization to non-declaratives in a generalization of truth-theoretic semantics that appeals to fulfillment conditions, of which truth conditions are one variety. On this approach, logical forms are not reified, and the notion of sameness of logical form is treated as conceptually basic. We discuss the relation of this conception of logical form to the project of identifying logical constants, reviewing two approaches, one of which takes topic neutrality as central, the other recursion. We argue that the project of identifying logical constants for the purposes of classifying together valid arguments is largely independent of that of identifying logical form of sentences, and urge an ecumenical approach to extending talk of logical constants beyond where it is currently well grounded. (shrink)

Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...) structure, because they differ in the placement of the logical constants “every” and “some”. By contrast, the sentences Every girl loves some boy. and Every boy loves some girl. are thought to have the same logical form, because “girl” and “boy” are not logical constants. Thus, in order to settle questions about logical form, and ultimately about which arguments are logically valid and which sentences logically true, we must distinguish the “logical constants” of a language from its nonlogical expressions. (shrink)

This paper does not deal with the topic of ‘the generosity of artificial languages from an Asian or a comparative perspective’. Rather, it is concerned with a particular case taken from a development in the Western tradition, when in the wake of the rise of formal logic at the end of the nineteenth and the beginning of the twentieth century people in philosophy and later in linguistics started to use formal languages in the study of the semantics of natural languages. (...) This undertaking rests on certain philosophical assumptions and instantiates a particular methodology, that we want to examine critically. However, that in itself is still too broad a topic for a single paper, so we will focus on a particular aspect, viz., the distinction between grammatical form and logical form and the crucial role it plays in how the relationship between natural languages and formal languages is understood in this tradition. We will uncover two basic assumptions that underlie the standard view on the distinction between grammatical form and logical form, and discuss how they have contributed to the shaping of a particular methodology and a particular view on the status of semantics as a discipline. But before we turn to the topic at hand, a few more words on the general nature of the investigation are in order. Its general aim is to find out how semantics constructs its object, i.e., we are interested in what semanticists view as the proper object of study, how they think this object can best be approached, and how they view the relations between their own undertaking and neighbouring disciplines that deal with related, or even the same kind of phenomena, such as cognitive psychology, cognitive neuroscience, philosophy, anthropology. The background assumption is that, much like in other disciplines, semantics, too, does not have its object of investigation cut out for itself by nature, but constructs it in a complex process that involves empirical elements (‘facts’ being already too dangerous a term), philosophical assumptions, and borrowings.... (shrink)

The LOGICAL FORM of a sentence (or utterance) is a formal representation of its logical structure; that is, of the structure which is relevant to specifying its logical role and properties. There are a number of (interrelated) reasons for giving a rendering of a sentence's logical form. Among them is to obtain proper inferences (which otherwise would not follow; cf. Russell's theory of descriptions), to give the proper form for the determination of truth-conditions (e.g. Tarski's method of truth and satisfaction (...) as applied to quantification), to show those aspects of a sentence's meaning which follow from the logical role of certain terms (and not from the lexical meaning of words; cf. the truth-functional account of conjunction), and to formalize or regiment the language in order to show that it is has certain metalogical properties (e.g. that it is free of paradox, or that there is a sound proof procedure). (shrink)

*I am very pleased to be able to contribute this paper to a festschrift for Andrea Bonomi. This is not however, the paper I really wanted to write; I would have much rather have contributed a paper comparing the pianistic styles of Lennie Tristano and Bill Evans, which I think Andrea would have found much more fascinating than an essay devoted to an understanding of Frege’s thinking. But I do not totally despair. Andrea’s first paper published in English was (...) entitled “On the Concept of Logical Form in Frege,” so perhaps I can maintain some hope that this paper will appeal to lingering interests that Andrea wrote of in the past. I would like to thank Johannes Brandl, Ben Caplan, Bill Demopoulos, Bob Fiengo, Mark Kalderon, Patricia Marino, Gila Sher, Michael Thau, Dan Vest and especially Aldo Antonelli for very helpful discussion. (shrink)

Over the years, I’ve been asked many times what “logical form” is, as applied to natural language. This is a natural enough question to address to me; after all, I’ve written a book titled Logical Form, and I’ve been asked to write any number of papers on the topic. This question, it seems to me, is certainly a “big” question, and big questions deserve big answers. I must admit, however, to being somewhat baffled as to how to do this satisfactorily, (...) since big answers to big questions unfortunately tend to the trivial. With a nod to Wittgenstein, logical form has always seemed to me to be something that you know it when you see it; it is clear enough when it pops up, but one is hard pressed to say just what it is, to define it. This is so even though the meanings of the words “logical” and “form” seem straightforward enough; what I find puzzling is how the first word is supposed to modify the second. What is it that makes a form logical, as opposed to something else that is not logical? This, it seems to me, is a very hard question to answer indeed, for if we cannot contrast logical form with some other type of form, then every form (or no form) is a logical form, and we have arrived at the triviality previously mentioned. (shrink)

Consider the following argument: All men are mortal; Socrates is a man; therefore, Socrates is mortal. Intuitively, what makes this a valid argument has nothing to do with Socrates, men, or mortality. Rather, each sentence in the argument exhibits a certain logical form, which, together with the forms of the other two, constitute a pattern that, of itself, guarantees the truth of the conclusion given the truth of the premises. More generally, then, the logical form of a sentence of natural (...) language is what determines both its logical properties and its logical relations to other sentences. The logical form of a sentence of natural language is typically represented in a theory of logical form by a well-formed formula in a ‘logically pure’ language whose only meaningful symbols are expressions with fixed, distinctly logical meanings (e.g., quantifiers). Thus, the logical forms of the sentences in the above argument would be represented in a theory based on pure predicate logic by the formulas ‘∀x(Fx ⊃ Gx)’, ‘Fy’, and ‘Gy’, respectively, where ‘F’, ‘G’, and ‘y’ are all free variables. The argument’s intuitive validity is then explained in virtue of the fact that the logical forms of the premises formally entail the logical form of the conclusion. The primary goal of a theory of logical form is to explain as broad a range of such intuitive logical phenomena as possible in terms of the logical forms that it assigns to sentences of natural language. (shrink)

In this paper I rehearse two central failings of traditional possible world semantics. I then present a much more robust framework for intensional logic and semantics based liberally on the work of George Bealer in his book Quality and Concept. Certain expressive limitations of Bealer's approach, however, lead me to extend the framework in a particularly natural and useful way. This extension, in turn, brings to light associated limitations of Bealer's account of predication. In response, I develop a more general (...) and intuitively more adequate account of the logical form of predication. (shrink)

A realist theory of truth for a class of sentence holds that there are entities in virtue of which these sentences are true or false. We call such entities ‘truthmakers’ and contend that those for a wide range of sentences about the real world are moments (dependent particulars). Since moments are unfamiliar we provide a definition and a brief philosophical history, anchoring them in our ontology by showing that they are objects of perception. The core of our theory is the (...) account of truthmaking for atomic sentences, in which we expose a pervasive ‘dogma of logical form’, which says that atomic sentences cannot have more than one truthmaker. The authors uphold the mutual independence of logical and ontological complexity. The theory is compared with that of Wittgenstein’s Tractatus, and the authors outline formal principles of truthmaking taking account of both kinds of complexity and suggesting how to overcome Wittgenstein’s problem of negation. (shrink)

Logic has its roots in the study of valid argument, but while traditional logicians worked with natural language directly, modern approaches first translate natural arguments into an artificial language. The reason for this step is that some artificial languages now have very well developed inferential systems. There is no doubt that this is a great advantage in general, but for the study of natural reasoning it is a drawback that the original linguistic forms get lost in translation. An alternative approach (...) would be to develop a general theory of the natural logic behind human reasoning and human information processing by studying formal logics that operate directly on linguistic representations. That this is possible we will try to make plausible in this paper. It will turn out that one level of representation, that of Logical Form, can meaningfully be identified with the language of an existing and well-understood logic, a restricted form of the theory of types. It is not difficult to devise inference systems for this language, and it is thus possible to study reasoning systems that are based directly on language. (shrink)

Type-logical semantics studies linguistic meaning with the help of the theory of types. The latter originated with Russell as an answer to the paradoxes, but has the additional virtue that it is very close to ordinary language. In fact, type theory is so much more similar to language than predicate logic is, that adopting it as a vehicle of representation can overcome the mismatches between grammatical form and predicate logical form that were observed by Frege and Russell. The grammatical forms (...) of ordinary language sentences consequently may be taken to be much less misleading than logicians in the first half of the 20th century often thought them to be. This was realized by Richard Montague, who used the theory of types to translate fragments of ordinary language into a logical language. Semantics is commonly divided into lexical semantics, which studies the meaning of words, and compositional semantics, which studies the way in which complex phrases obtain a meaning from their constituents. The strength of type-logical semantics lies with the latter, but type-logical theories can be combined with many competing hypotheses about lexical meaning, provided these hypotheses are expressed using the language of type theory. (shrink)

Yah boo sucks to the grammer wot we lernt in skool! Grammar (and the bad old traditional logic) says that quantifier phrases such as 'nobody', 'everyone', 'all women', 'some men' and 'a man' are in the same category as names such as 'Milly', 'Molly' and 'Mandy'. So, prior to their first corrective lessons, students are awfully muddled, the first and fundamental problem being the Woozle hunt for somebody called 'nobody'. Hoorah for modern logic and logic teachers! The story used to (...) justify our current logics is entirely fictional. The claims about names and quantifier phrases in English are wildly false. Two of the heroes of modern logic, Russell and Hilbert, make the very mistakes which are falsely blamed on traditional logic. The villain, Meinong, turns out to have been working a different patch. Ideas ascribed to traditional grammar are modern inventions. Neither logicians nor grammarians can be trusted to tell the history of either grammar or logic. (shrink)

That behind the overt, syntactic structure of an expression there lurks a covert, semantic one, aka logical form, and that anyone interested in what the expression truly means should ignore the former and go for excavating the latter, has become a common wisdom. It is this wisdom I want to challenge in this paper; I will claim that it is a result of a mere confusion, that the usual notion of semantic structure, or logical form, is actually the result of (...) certain properties of our tools of linguistic analysis being unwarrantedly projected into what we analyze. (shrink)

Paul M. Pietroski, University of Maryland For any sentence of a natural language, we can ask the following questions: what is its meaning; what is its syntactic structure; and how is its meaning related to its syntactic structure? Attending to these questions, as they apply to sentences that provide evidence for Davidsonian event analyses, suggests that we reconsider some traditional views about how the syntax of a natural sentence is related to its meaning.

Introduction 1.1 GOALS This book is devoted to an in-depth investigation of some of the properties of Logical Form (LF). In particular, the primary aim of ...

By a logical theory I mean a formal system together with its semantics, meta-theory, and rules for translating ordinary language into its notation. Logical theories can be used descriptively (for example, to represent particular arguments or to depict the logical form of certain sentences). Here the logician uses the usual methods of empirical science to assess the correctness of his descriptions. However, the most important applications of logical theories are normative, and here, I argue, the epistemology is that of wide (...) reflective equilibrium. The result is that logic not only assesses our inferential practice but also changes it. I tie my discussion to Thagard's views concerning the relationship between psychology and logic, arguing against him that psychology has and should have only a peripheral role in normative (and most descriptive) applications of logic. (shrink)

Most philosophers of language with an interest in epistemology would have said, until very recently, that an utterance of (1) semantically expresses a proposition that is true if and only if Holmes ( h ) and the proposition that Mary stole the bicycle ( p ) are related by the binary relation of knowing (K xy ), so that the logical form of (1) is K hp . But in the past few years, a few plucky epistemologico-linguists, most notably Jonathan (...) Schaffer, have tried to defend a contrasting view that has come to be known as “contrastivism”. (shrink)

This paper focuses on the inferential configuration of arguments, generally referred to as argument scheme. After outlining our approach, denominated Argumentum Model of Topics (AMT, see Rigotti and Greco Morasso 2006, 2009; Rigotti 2006, 2008, 2009), we compare it to other modern and contemporary approaches, to eventually illustrate some advantages offered by it. In spite of the evident connection with the tradition of topics, emerging also from AMT’s denomination, its involvement in the contemporary dialogue on argument schemes should not (...) be overlooked. The model builds in particular on the theoretical and methodological perspective of pragma-dialectics in its extended version, reconciling dialectic and rhetoric; nevertheless, it also takes into account numerous other contributions to the study of argument schemes. Aiming at a representation of argument schemes able to monitor the inferential cohesion and completeness of arguments, AMT focuses on two components of argument scheme that could be distinguished, readapting pragma-dialectical terms, as procedural and material respectively. The procedural component is based on the semantic-ontological structure, which generates the inferential connection from which the logical form of the argument is derived. The material component integrates into the argument scheme the implicit and explicit premises bound to the contextual common ground (Rigotti 2006). In this paper, the comparison of the AMT to other approaches focuses on the inferential configuration of arguments and not on the typologies of argument schemes and on the principles they are based on, which the authors intend to tackle in a further paper. (shrink)

Quine’s criticism of the notion of analyticity applies, at best, to Carnap’s notion, not to those of Frege or Husserl. The failure of logicism is also the failure of Frege’s definition of analyticity, but it does not even touch Husserl’s views, which are based on logical form. However, some relatively concrete number-theoretic statements do not admit such a formalization salva veritate. A new definition of analyticity based not on syntactical but on semantical logical form is proposed and argued for.

In the works of Kant and his followers, the notion of form plays an important role in explaining the apriority, necessity and certainty of logic. Bernard Bolzano (1781–1848), an important early critic of Kant, found the Kantians' definitions of form imprecise and their explanations of the special status of logic deeply unsatisfying. Proposing his own conception of form, Bolzano developed radically different views on logic, truth in virtue of form, and other matters. This essay presents Bolzano's views in the light (...) of his criticisms of the Kantian logicians. (shrink)

Standard compositionality is the doctrine that the semantic content of a compound expression is a function of the semantic contents of the contentful component expressions. In 1954 Hilary Putnam proposed that standard compositionality be replaced by a stricter version according to which even sentences that are synonymously isomorphic (in the sense of Alonzo Church) are not strictly synonymous unless they have the same logical form. On Putnam’s proposal, the semantic content of a compound expression is a function of: (i) the (...) contentful component expressions; and (ii) the expression’s logical form. Kit Fine recently expanded and modified Putnam’s idea into a sweeping theory in philosophy of language and philosophy of mind. The present paper is a detailed critique of Fine’s “semantic relationism.” Fine’s notion of coordination is explained in terms of the familiar pragmatic phenomenon of recognition. A serious error in Fine’s formal disproof of standard Millianism is exposed. It is demonstrated furthermore that Church’s original criticism of Putnam’s proposal can be extended to Fine’s semantic relationism. Finally, it is also demonstrated that the positive position Fine proffers to supplant standard Millianism is in fact exactly equivalent to standard Millianism, so that Fine’s overall position not only does not displace standard Millianism but is in fact inconsistent. (shrink)

Abstract The paper presents an outline of a unified answer to five questions concerning logic: (1) Is logic in the mind or in the world? (2) Does logic need a foundation? What is the main obstacle to a foundation for logic? Can it be overcome? (3) How does logic work? What does logical form represent? Are logical constants referential? (4) Is there a criterion of logicality? (5) What is the relation between logic and mathematics?

In this paper I examine a cluster of concepts relevant to the methodology of truth theories: ‘informative definition’, ‘recursive method’, ‘semantic structure’, ‘logical form’, ‘compositionality’, etc. The interrelations between these concepts, I will try to show, are more intricate and multi-dimensional than commonly assumed.

Despite some talk of ‘erotetic logic’ and ‘the logic of interrogatives’, logicians have hitherto completely overlooked the peculiar logical form of questions, also shared by interrogative clauses generally. Of relevance to an understanding of time are those interrogative clauses that are janus-like: sometimes raising a question, sometimes answering it—which can then no longer arise. Since a closed question can no longer arise, it might seem that simply the passing of time turns an open into a closed question. Instead, the passing (...) of time itself can be understood as the closing or resolution of open questions, of the determination of what is not fixed but as yet in question. (shrink)

Vernacularism is the view that logical forms are fundamentally assigned to natural language expressions, and are only derivatively assigned to anything else, e.g., propositions, mental representations, expressions of symbolic logic, etc. In this paper, we argue that Vernacularism is not as plausible as it first appears because of nonsentential speech. More specifically, there are argument-premises, meant by speakers of non-sentences, for which no natural language paraphrase is readily available in the language used by the speaker and the hearer. The speaker (...) can intend this proposition and the hearer can recover it (and its logical form). Since they cannot, by hypothesis, be doing this by using a sentence of their shared language, the proposition-meant has its logical form non-derivatively, which falsifies Vernacularism. We conclude the paper with a brief review of the debate on incomplete definite descriptions in which Vernacularism is assumed as a suppressed premise. (shrink)